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NASA CONTRACTOR

REPORT

COCO

PS

I N A S A C R - 2 1 3 3

(NASACRORTMXOR AD NUMBER)

HIGH PERFORMANCES-BAND HORN ANTENNASFOR RADIOMETER USE

by R. Caldron, C. A. Mtntzer, L. Peters, and J. Toth

Prepared by

THE OHIO STATE UNIVERSITY

ELECTROSCIENCE LABORATORYColumbus, Ohio 43212

Jor Langley Research Center

NATIONAL AERONAUTS AND SPACE ADMINISTRATION • WASHINGTON, D. C.J A N U A R Y 1973

https://ntrs.nasa.gov/search.jsp?R=19730007408 2020-03-23T02:09:25+00:00Z

1. Report No. 2. Government Accession No.NASA CR-2133

4. Title and Subtitle

HIGH PERFORMANCE S-BAND HORN ANTENNAS FOR RADIOMETER USE

7. Author(s)

R. Caldecott, C. A.^Mentzer, L. Peters and J. Toth

9. Performing Organization Name and AddressThe Ohio State UniversityElectroScience LaboratoryColumbus, Ohio kj212

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, B.C. 205^6

3. Recipient's Catalog No.

5. Report DateJanuary 1973

6. Performing Organization Code

8. Performing Organization Report No.

10. Work Unit No.

160-20-5^-0311. Contract or Grant No.

NAS1-10C&0

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract

Horn antennas of four types: pyramidal corrugated, conical corrugated, pyramidal dual modeand conical dual mode, have been constructed and evaluated for use as S-band radiometerantennas. Each of the structures is described and radiation patterns and impedance and resistiveloss measurements including a layer of foreign material on a thin radome, are presented. Aprecision method for determining reflection losses is described using a multiprobe reflecto-meter technique. The same technique is also applied to the measurement of resistive lossesby closing the ends of the antennas with short circuit plates and determining the losses froman accurate measurement of the reflection coefficient. The radiation patterns were recordedwith the aid of a real-time digital computer. The stored patterns were then processed to yieldgain and beam efficiency.

It was concluded that it is possible to design a highly efficient antenna for radiometeruse and to measure its parameters precisely. However, it was found that it is necessary tomodify the conventional definition of beamwidth somewhat if this term is to be meaningful forradiometer applications.

17. Key Words (Suggested by Author(s))

Antennas Radiometer Antennas, Corrugated

Horn Antennas

18. Distribution Statement

Unclassified - Unlimited

19. Security Qassif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price*

Unclassified Unclassified 110 $3.00

' For sale by the National Technical Information Service, Springfield, Virginia 22151

PRECEDING PAGE BLANK NOT FILMED

TABLE OF CONTENTS

Page

I. INTRODUCTION 1

II. DISCUSSION OF THE REQUIRED PARAMETERS 2

III. ANTENNA TYPES AND RADIATION PATTERN CHARACTERISTICS 3

A. The Conical Corrugated Horn Antenna 4B. The Pyramidal Corrugated Horn Antenna 9C . T h e Conical Dual Mode Horn A n t e n n a 2 5D. The Pyramidal Dual Mode Horn Antenna 38E. Comparisons with a Paraboloidal Antenna 38

IV. MEASURING TECHNIQUES . 43

A. The Reflectometer System 43T O T h e three probe reflectometer 45(ii) The four probe reflectometer 48(iii) Self checking systems 50

B. Impedance Measurements 53C. Resistive Loss Measurements 57D. Beam Efficiency Measurements 63

V. NEAR FIELD STUDIES 65

VI. RADOME LOSS MEASUREMENTS 78

VII. GEOMETRICAL DIFFRACTION THEORY APPLIED TO DUALMODE HORN DESIGN 100

A. The Pyramidal Dual Mode Horn 101B . T h e Conical Dual Mode H o r n 1 0 1

VIII. CONCLUSIONS 106

REFERENCES 108

I. INTRODUCTION

The objective of this program has been to design a horn antenna 'Ofhigh quality for use with an S-band radiometer. The antenna is tohave a symmetrical circularly polarized beam with a half-power beam-width of 25°. In itself, this is not too difficult a task. However,the ultimate intention of this research is to examine the limitationsintroduced by the antenna for radiometer systems with a capability ofobserving noise temperatures to an accuracy of better than 1°K. Thisrequires that the field of view of the antenna must be controlled andknown to a very high degree of accuracy. The term field of view isused here in a very broad sense. Of course it includes the field ofinterest, that which lies within the main beam. In addition it includesthe side and backlobes. If these are not to introduce substantial errors,they must be kept to an absolute minimum, i.e., the beam efficiency must behigh. A further contributor to the observed noise, though not viewedby the antenna in the conventional sense, is resistive loss within theantenna structure. The contribution from this source depends on theloss (or alternatively the emission coefficient) of the antenna and onits physical temperature. If both these are known, a correction canbe made. Thus, while it is not necessary to keep the loss extremelylow (though this simplifies the measurement problem), it is necessaryto evaluate it with a high degree of accuracy. A final contributor tothe noise observed by the antenna results from its own mismatch. Anynoise originating in the front end of the radiometer will be partiallyreflected back into the system by any mismatch at the antenna terminals.The effect is similar to that of the resistive loss. If the magnitudeof the mismatch and the temperature of the radiometer front-end areknown then correction can be made. However, it is first desirable tokeep the mismatch to a minimum and then to know the residual mismatchto a high degree of accuracy.

It is evident from the foregoing that both the design of a highquality antenna and a precision evaluation of its characteristics arerequired. Target parameters for the antenna design were a symmetricalbeam with a half-power beamwidth of 25°, sidelobes below 30 dB (preferably35 dB), and a beam efficiency in the order of 97%. The target forevaluation of loss and mismatch was 0.01 dB. If such loss were assumedto occur at 3000K, 0.01 dB would correspond to an accuracy of 0.72°K.The 0.01 dB figure is the permissible loss of radiated power referredto the input power if the antenna were operating as a transmitter.

II. DISCUSSION OF THE REQUIRED PARAMETERS

Some of these parameters appear to be rather awesome and othersdepend on the definition of the quantity. The 0.01 dB accuracy figureof the antenna matching can be satisfied if the antenna VSNR is keptbelow 1.1. The antenna absorption losses must of course be measured toan accuracy of 0.01 dB of the forward power in the antenna, whentransmitting.

Satisfaction of the beam efficiency condition depends on howthe beam efficiency is defined. The common definition consisting ofthe ratio of the power radiated in the main beam (the region enclosedby the first null) to the total power radiated is not applicable toantenna patterns void of nulls, since this definition would alwaysgive 100% beam efficiency. An alternate definition for the beamefficiency B of the form

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where S is the transmitted power density, is suggested. For example,the main beam may be fixed arbitrarily so that it includes twice thehalf power beamwidth, i.e., 6] = e^pg^. If the back lobe radiationis taken at a practical level of 40 dB below the pattern maximum forthis half power beamwidth, this leads to an efficiency on the order90% for the case of a rotationally symmetric pattern of the form, ofthe H-plane pattern. (Further decreasing the back lobe level hasonly a minor effect on the beam efficiency.) Increasing the regionof the main beam to include three times the half-power beamwidth(ei = 1.5 x QHPBW) yields a 99% beam efficiency. These values arerelatively independent of the aperture phase taper (or H-plane horngeometry) once the phase distribution is such that the desired H-planeantenna pattern is obtained. This rotationally symmetric antenna patterncan be obtained, and is needed to obtain the desired circular polarizationover the main beam. In other words, the area to be observed or the"footprint" should be the angular region covered by approximately 35°from the polar axis for this particular low side lobe antenna to maintainthe desired beam efficiency. Also it is only necessary to maintain thecircular polarization over this angular region corresponding approximatelyto the -15 dB pattern level. These requirements appear too excessive inthat the extent of the footprint would be almost twice the altitudeof the antenna. Of course, the contribution from the extreme edgesof the footprint would be reduced by the pattern level(-15 dB) butwould look at a larger area per increment of polar angle. The use ofa narrower antenna beam would require a larger aperture and a longerhorn but a lower backlobe radiation level can be achieved. Thisreduces the angular extent required to achieve the 99% efficiency.

It should be noted that while backlobes 40 dB below the main beamproduce a negligible effect on the present antennas, this would not betrue for antennas with a narrower beam. The narrower beam antennahas a higher gain and therefore, though the absolute level of thebacklobe radiation remains the same, the level relative to the mainbeam will be lower. For 1% radiation in the back pattern, the approxi-mate back lobe level in dB, relative to the main beam, is given by:

DB = 10 log1Q4TT

Beam Area Within Half Power Points + 17

III. ANTENNA TYPES AND RADIATION PATTERN CHARACTERISTICS

The requirements for this application are a symmetrical circularlypolarized beam with low side and backlobes. The requirement of symmetryobviously suggests a symmetrical antenna structure. The H-plane patternof a simple horn has the desired characteristics: namely low side andbacklobes. These result from a tapered aperture distribution, whichreduces the sidelobes, and zero field at the horn walls which, sinceit reduces edge diffraction at the aperture, minimizes the sidelobesand backlobes. All of the antenna types considered are designed toproduce a similar field configuration in the E- as well as the H-plane.

Two basic methods were used to produce the desired taper in the ,E-plane. The first of these employed the concept of a corrugated surfaceto suppress the surface ray along the E walls. In this method slotsare cut into the walls normal to both the surface and the directionof propagation. These slots are between a quarter and a half wave-length in depth and are therefore capacitive. It has been establishedfor rectangular waveguides that the boundary conditions cannot besatisfied for the case where the surface impedance is capacitive for 2all four walls. However, it is suggested by an analysis by Narashimhanthat this concept is not valid for the pyramidal horn geometry. Excellenthorn performance has been achieved with corrugations on all four walls ofa pyramidal horn. The hybrid modes in a circular corrugated horn arewell defined modes. A balanced hybrid mode theory has been developedfor the circular corrugated horn which has been applied to the case 3 „where corrugations are exactly A/4 deep. However, several experiments 'have shown the horn is an excellent radiator over nearly a two to onebandwidth. Moreover, the reported input VSWR is quite high when thecorrugations are A/4 deep. At this time, the theory has not beendeveloped to include the operation of the horn in the more appropriateoperating band. The detailed design of these antennas and their per-formance characteristics are presented in a later section of thisreport.

The second method used to generate symmetrical E- and H-planepatterns was the dual mode technique5. In this method, a higher ordermode is generated in the horn in addition to the fundamental mode.This is selected so that it undergoes one and a half phase reversalsacross the width of the aperture, and is in phase with the fundamentalmode at the center while exactly cancelling at the edges. A circularhorn has been constructed based on this principle. The modes in thiscase are the fundamental TE-|] mode with the TMn used to produce thedesired taper. The TM-n mode is generated by a step in the throat ofthe horn. A square dual mode horn was also constructed and tested.This horn was essentially similar in construction employing the fundamentalTEoi mode with a blend of the TM;?i and the TE21 used to produce the desiredtaper. The field configuration in this case bears a strong physical re-semblance to that in the circular dual mode horn. Design details andperformance data for these horns will also be presented.

A. The Conical Corrugated Horn Antenna

The measured amplitude of the electric field in the aperture of theconical corrugated horn fits a cosine distribution in both the E- andthe H-planes. Thus standard H-plane conical horn curves such as thosegiven by Jasik^ may be used to obtain the pattern in the vicinity of themain beam for a conical corrugated horn. The "optimum horn" with diameter3.4A and slant length 3.9A was selected since it presented a compromiseon physical size and pattern qualities. This resulted in an aperture25.4 cm in diameter and a 56° flare angle.

From past experience, good antenna patterns are obtained for cor-rugation depths between x/4 and A/2 and for more than five corrugationsper wavelength for a horn several wavelengths long. Eight corrugationsper wavelength and a corrugation depth of 0.43A were chosen for thisrelatively short horn. The corrugation depth has little effect on theradiation pattern in the range 0.25 <_ d/A <_ 0.375 but affects the antennaimpedance. For depths approaching 0.5A the radiation pattern deterioratesslightly while the impedance match improves. The .0.43A depth was chosento yield Tow VSWR. The antenna, pictured in Fig. 1, was .machined froman aluminum billet specially cast for this purpose.

Aperture distribution measurements at 3.7 GHz, both amplitudeand phase, appear in Figs. 2, 3 and 4 for cuts corresponding to theH-plane, E-plane and 45° plane respectively. These measurements wereobtained using a nulled radar system and probing .the fields with asmall sphere. These data show that, in the aperture, the phase frontis essentially that of a point source at the cone vertex.' Calculatedphase points for this assumed phase center are shown for comparison.It is interesting to note that this horn has an aperture distributionwhich is nearly circularly symmetrical about its axis. Thus its farfield patterns should also be nearly symmetrical.

Fig. 1. The conical corrugated horn antenna,

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The E and H plane radiation patterns for the antenna are shown inFig. 5. These were recorded using a digital computer to store the data.Patterns were recorded in planes at 22%° intervals in addition to the Eand H planes. The average pattern of these various cuts for both paralleland crossed polarization is shown in Fig. 6. Averaging was performed inthe computer after all the patterns had been recorded. The data werefurther processed to yield beam efficiency, defined here as the fractionof the total radiated power (the antenna is considered to be transmitting)contained within a cone of any given angle from the beam axis. The crosspolarized energy may be considered as desirable or undesirable dependingon the particular application. The beam efficiency was therefore calcu-lated both ways and is presented in Figs. 7 and 8.

In Fig. 5 shoulders are apparent at -27 dB on the E-plane pattern.At lower frequencies, these are lower while at 3.9 GHz the shouldersare at -23 dB. These shoulders illustrate the pattern deteriorationas the corrugation depth approaches A/2 at 4.28 GHz. This slight com-promise in radiation pattern was made to obtain a good impedance match.An expanded radiation pattern of the main beam at 3.9 GHz with theantenna set up to receive circular polarization appears in Fig. 9.Shown here is the received pattern for vertical transmitted polarization,and, at selected points, lines obtained by rotating the transmitted polari-zation 180° while the receiving antenna is stationary. The length of thisline is 20 log b/a where "b" and "a" are the major and minor axes of thepolarization ellipse. The axial ratio is approximately 1.8 in the regionof 30°.

B. The Pyramidal Corrugated Horn Antenna

A pyramidal corrugated horn with a 56° flare angle and 10 inchessquare aperture was built. The horn, shown in Fig. 10, is fed by a1-3/4 inches square waveguide and has corrugations which are 0.43A deepat 3.8 GHz on all four walls. The large flare angle and deep corrugationswere chosen, as in the case of the conical corrugated horn, to obtain acompact antenna and to provide a good impedance match, possibly at thecost of some slight deterioration in the radiation pattern.

Radiation patterns obtained with this antenna at 3.9 GHz areshown in Fig. 11. The H-plane pattern shows good agreement withtypical horn design curves and changes only slightly from 3.8 GHzto 4.0 GHz. The E-plane pattern, however, is wider (28° at the 3 dBpoints) than the H-plane pattern (26° at the 3 dB points). It wasalso observed that this horn's E-plane radiation patterns exhibiteda greater frequency dependence than expected. For example, at 4.0GHz, the main beam sharpens up to match the 23° H-plane beamwidthwhile at 3.8 GHz a shoulder appears at -7 dB. Past work on cor-rugated horns has indicated that the frequency dependence should bemuch less than observed. For example, an X-band horn with two wallscorrugated had nearly equal E- and H-plane beamwidths at both 3 and10 dB over almost a 2:1 frequency range. At this point, the reasonfor this frequency dependence was not definitely known but was thoughtto be associated with the number and depth of the corrugations andpossibly the short length of the horn.

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This non-stationary behavior of the E-plane pattern is evidentlycaused by higher order modes which are generated at the position wherethe corrugations are initiated. If the surface could be truly repre-sented by the capacitive impedance condition, these modes should besufficiently attenuated. This is indicated by earlier measurementsmade by Peters and Lawrie^ for a horn of nearly the same geometry.The major difference was that their horn had 15 teeth per wavelengthat the center frequency in lieu of the 6 teeth per wavelength for thishorn. To further validate this conclusion that the number of teeth issignificant, a longer horn with 6 teeth per wavelength was considered.This was an X-band horn with the desirable property of nearly identicalE and H plane patterns, a 29° flare angle instead of the previous 55°,and 8.75 inches long. The patterns for this horn together with thecomputed average patterns and efficiency curves are shown in Figs. 12-15.The end of this horn was then removed to make it approximately the samelength as the above horn and again the same erratic behavior of theE-plane pattern appeared.

The conclusion then was that the corrugation density should beincreased. A horn geometry was constructed having the same pro-portions as the original horn, except for the number of corrugationsper wavelengths which was set at 15. The horn size was scaled downby a factor of 2^ to facilitate machining and the measurements madeat X-band. Radiation patterns were measured at a frequency intervalof 500 MHz from 8.5 to 11.5 GHz. The back level was maintained at-40 dB or lower over the entire frequency band. The E-plane patternswere substantially improved when compared to the patterns of con-ventional E-plane horns. While there was somewhat less variation inthe E-plane pattern than before, the beamwidth still varied. The twomost extreme patterns are shown in Figs. 16 and 17. It is interestingto note that they occur quite close in frequency, the E-plane changingfrom being wider than the H-plane to being narrower quite quickly.A further change in frequency in either direction produces a slow changein beamwidth back to the other condition. The most symmetrical patternwas obtained at 8.95 GHz and is shown in Fig. 18. The .computed averagepatterns and beam efficiency for this case are shown in Figs. 19-21.

It is evident from these measurements that the pyramidal cor-rugated horn has a less stable mode structure than the conical cor-rugated horn. In order to achieve a symmetrical beam over a wideband it is necessary to use a low flare angle and a relativelylarge number of corrugations. It appears that the number of cor-rugations per wavelength is less important than the total numberpresent.

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C. The Conical Dual Mode Horn Antenna

A dual mode horn was constructed based directly on the designdescribed by Potter.5 The dimensions of the step and aperture werescaled directly from those given in Reference 5 with a further adjustmentof the aperture width to yield the desired beamwidth. Some further changeswere made, however, to reduce the overall size of the horn as far as possible.Potter found empirically that when the TM]] mode was generated at the step,it differed in phase from the fundamental TE-|] mode by about 0.16A. Hetherefore arranged the flare and an additional cylindrical section toyield an additional differential phase shift between the two modes ofabout 1.84x between the step and the aperture to produce the desiredaperture distribution. To minimize the length, the present horn wasdesigned with an additional differential phase shift of only 0.84A.Since the aperture and step dimensions were already determined thisresulted in a flare angle of 10.4°. The same angle was used for thetransformer section between the input waveguide and the step. Therewas no particular reason for using the same angle other than it seemedreasonable for the purpose. The transformer taper was felt to be suf-ficiently gradual that the cylindrical section prior to the step, usedby Potter as a mode filter, could be omitted. The dimensions of theresulting horn are shown in Fig. 22 and a photograph in Fig. 23. Thethroat section was machined from solid stock. The flare section wasrolled from sheet and welded. Two annular ribs were welded to theoutside (one of these is visible in Fig. 23), also a threaded ring tomate with the throat section, the junction being at the step. Afterwelding the inside of the flare was machined to the final dimensions.

The radiation patterns for the Conical Dual Mode Horn for linearpolarization at a frequency of 3.8 GHz are shown in Fig. 24. Thecomputed average patterns and beam efficiency curves are shown inFigs. 25-27. Figure 28 shows the C.P. performance at 3.9 GHz. Thefigure shows the main beam on an expanded scale with the horn set upto receive C.P. The transmitter was linearly polarized. At a numberof points in the pattern the receiving antenna was stopped and thetransmitter polarization rotated. The vertical lines so produced in-dicate the ellipticity of the polarization. The best C.P. for this hornwas obtained at 3.8 GHz as shown in Fig. 29. The C.P. at 4.0 GHz wassimilar to that at 3.9 GHz.

At 3.8 GHz, the polarization is comparable or slightly superior tothat of the conical corrugated horn. However, for 0.1 GHz shift infrequency, the polarization properties deteriorate to an axial ratioof the order of 10 dB at an angle of 30°. The beam efficiency is alsobetter than that of the conical corrugated horn at 3.8 GHz. This resultsfrom the presence of a null in the radiation pattern, which does not existfor the corrugated horn pattern, producing a sharper fall off at the beamedge. Again, of course, it should be stressed that the dual mode horn isa much narrower band structure.

The aperture distributions for the conical dual mode horn are shownin Figs. 30 and 31 for the H- and E-planes respectively.

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D. The Pyramidal Dual Mode Horn Antenna

In order to complete the quartet of antenna types a square dualmode horn was also constructed. Since Potter had found it necessary toadjust the phase of the various modes empirically for the circular dualmode horn, it was decided that to avoid a tedious trial and error designprocedure an attempt should be made to "square" the conical horn.

In the conical horn, the fundamental mode is the TEn and the higherorder mode used to produce the desired aperture taper is the TMn.These should have the same amplitude and phase at the aperture. In thesquare horn the fundamental mode is the TEoi. If the TE-|2 and TMi2are now generated, each at half the amplitude of the TEoi mode a fieldconfiguration results which is very similar to that in the circulargeometry. It was decided that the most critical factors in generatingthe modes in the correct proportions and phases were the area ratioof the waveguides across the step and the guide wavelength for the higherorder modes after the step. The guide wavelength of the fundamental modeis relatively insensitive to guide size at this point since the guidedimension is considerably greater than that which will produce cut off.The guide size after the step was thus chosen to produce the same guidewavelength for the TEi2 and TMi2 modes as existed in the circular hornfor the TMn mode. This resulted in a guide of 3.706 inches on a side.The area ratio across the step was made the same which resulted in thesmaller dimension at the step being 2.895 inches. The aperture of thehorn was set to give the same 25° half power beamwidth based on a taperedaperture distribution and resulted in a dimension of 8.563 inches. It wasfurther assumed that a differential phase shift between the step and theaperture of 0.84X would be required as before. This resulted in a flareangle of 9.795° and a length of 14.07 inches from the step to the aperture.A 3.0 inch long taper was used to feed the step section from the 1.75 inchwaveguide.

This horn was constructed using quarter inch aluminum sheet forthe sides of the large section and brass for the step and taper sections.The resulting antenna patterns are shown in Fig. 32 for a frequency of3.7 GHz which was found to be the best frequency for this particularhorn. The average patterns and beam efficiency curves are shown inFigs. 33-35.

E. Comparisons with a Paraboloidal Antenna

In order to show how much better all of the antennas just discussedare for the intended application than the ever popular paraboloid somecomparative measurements of beam efficiency were made. It should bementioned that the antenna used for comparison is not a particularlygood specimen for the purpose since it has a rather small focal lengthto diameter ratio (1:4). A shallow reflector would show a better per-formance since the feed would have a better defined phase center overthe extent of the parabola. It was selected because its 14 inch diametergives approximately the same beamwidth as the other antennas tested and

38

because it was equipped with a dipole feed suitable for use at 3.7 GHz.Its radiation patterns and beam efficiency curves are shown in Figs. 36-39. It will be noticed that the beam efficiency is very low, less than60%. This is in part due to the quality of this particular antenna,but mainly due to the high side lobes which do not exist on the otherantennas. However, 65 to 68% is about the maximum obtainable from aparaboloid. The cross polarized radiation is also very high. Thisagain is in part due to the low f/d ratio. It is impossible to obtaina beam efficiency of 90% at any angle because of the cross polarizedcomponent.

In summary it may be said of the pattern characteristics of theantenna types tested that:

(a) For wide band applications the corrugated structures performbest, i.e., bandwidths of 50% or greater.

(b) For narrower band (5%) the dual mode structures have theadvantage of a sharper drop off in the beam skirts, probablydue in part to the smaller flare angle. Thus the percentageof power contained in twice the half-power beamwidth isgreater.

(c) The circular structures have a lower cross polarized componentof radiation than do the square structures and they may be°xpected to perform better in a circularly polarized system.

(d) The square corrugated structures for these small wide flareangle horns have been found to be critically dependent on:flare angle, total number of corrugations, and number ofcorrugations per wavelength. Considerable care must beexercised in the choice of these parameters to obtainproper performance.

(e) All the antennas tested far out perform such well knownbasics as the paraboloid.

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42

IV. MEASURING TECHNIQUES

As indicated in the introduction, a major part of the program atleast as important as antenna design is the precise evaluation of theresulting antennas. In addition to reducing reflection and resistivelosses to a minimum, it is necessary that the residual losses be measuredto 0.01 dB (referred to the forward power when the antenna is operatedin a transmitting mode). Further, a beam efficiency of around 97% isneeded which in turn requires a method capable of measuring efficienciesof this order. The methods developed for making measurements of therequired accuracy will now be described.

A. The Reflectometer System

A fundamental problem in the present case is that all the antennasbeing considered use either round or square waveguide and no slotted linesor other reflection measuring devices are commercially available for thesegeometries. If the voltage reflection coefficient is kept below 1.1 thenthe reflected power will be less than 0.01 dB of the incident power andthe accuracy is unimportant. However, as the reflection goes up theaccuracy becomes more of a problem and the reflection coefficient p mustbe measured to within approximately 0.0012/p. Even with the best slottedline available the necessary transformers would preclude sufficient ac-curacy.

One possibility is to construct a special slotted line in the wave-guide used for the antennas. However, this requires very close tolerancesand two such lines would have to be made. In addition, the presence of aslot in the waveguide is somewhat objectionable since it prevents circularpolarization being used with the slotted line in place. To overcome thisproblem use was made of a method originally proposed for plasma sheathdiagnostics, and further developed for the present purpose, employinga multiprobe reflectometer. The multiprobe ref1ectometer consists ofnothing more than a number of fixed probes loosely coupled to the wave-guide in much the same way as the single moveable probe of the slottedline. Each of the probes is connected to the measuring system via asquare law detector. It is necessary to assume that the coupling factorof each probe to the waveguide is the same or to provide an appropriatecalibration curve. In the present application a single probe mounted ina saddle, which could be placed on the waveguide in any of four locations,was used (Fig. 40). It was then only necessary for the probe to enterthe waveguide to the same depth in each position for the four probepositions to be considered identical. Additional holes were providedin the perpendicular plane for C.P. studies. It is also necessary forthe detectors to be square law or to be calibrated. However, forsmall VSWR's most detectors will easily satisfy the square lawrequirement.

43

Fig. 40. The four-probe reflectometer.

(i). The three probe reflactometer

Consider first a situation where the frequency is known but thejent power and the phase and amplitude of the reflection coefficient

are not known. There are three unknowns and the outputs from three probesare in general sufficient to evaluate them. There is one restriction andthat is that no two of the probes shall be spaced at any multiple of A/2.Otherwise the spacing of the probes is quite arbitrary, except for somepractical limitations on accuracy which will be discussed later. Let VI ^ the incident voltage and Vn the standing wave voltage on the transmissionline at the location of the nth probe. Then:

j(e-<j> )(1) V = V(l + Pe

n )

(2) |VJ2 = V2{1 + P2 + 2P cos (e-<j>n)}

where p and e are the modulus and angle of the reflection coefficient ofthe load and <j>n is the phase shift corresponding to the distance fromthe probe to the load and back, where <j> is taken as positive. Then:

(3) |Vn|2 = V2{1 + 02 + 2p (sin e sin 4>n + cos e cos <}>n)

or, writing sin <fin = Sp and cos <j>n = C where S and C are constantsfor a given probe configuration,

(4) |Vn|2 = V2{1 + P

2 + 2P (Sn sin e + Cn cos e) .

It is worth noting at this point that if square law detectors areused for the probes the output from the nth probe will in fact beproportional to |V |s If for convenience we now write:

(5) A = 2V2P cos e

(6) B = 2V2P sin e

(7) D = V2(l + P2)

(8) Pn - |VJ2

45

then for n = 1, 2 and 3 we have from Eq. (4):

(9) D + A + S^ - P1 = 0

(10) D + C2A + S2B - P2 = 0

(11) D + C3A + S3B - P3 = 0

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and

(15)P1 si

Now from Eqs. (5) and (6):

(16) e = arctan

07) P =+ B

and using Eq. (7)

46

(18) V2( 1 +A V 1= D

or

(19) V2 = D-±V/D - A - B

The root associated with the positive sign must be correct since ifP = 0

(20) A2 + B2 = 0 and V2 = D.

Therefore

(21) V2 = l/2{ D +V/D2 - A2 - B2 }

and p may be found from Eq. (17).2

V , it should be noted, is proportional to the forward power andmay be used as a measure of relative power level. With appropriatecalibration it may be used to measure absolute power.

So far the treatment has been entirely general, no particularrelationship between the probes being assumed. It will be noticedthat Eqs. (13), (14), and (15) are symmetrical in 1, 2, and 3, as isto be expected for arbitrary probes. In a practical reflectometer,however, the probes will generally be spaced at equal intervals. Thenlet

(22) <(,3 -

and

(23) <j>1 - ij»3 = -2<j>s, probe number 1 being nearest the load (Fig. 41),

47

H<

PROBE3

PROBE2

PROBE1

LOAD

Fig. 41. A reflectometer with 3 equally spaced probes.(4. denotes the two way phase angle betweenindicated points.)

Equations (14), (15), and (16) then take the form

P1(s3-s2) + P2i(24) A = -

-s3)2 sin (j> - sin 2<j>

(25) 6 =P,(C~ - C9) + P9(C, - CJ + P,(C9 - C,)

2 sin * - sin 2$

(26)sin

D =sin 2<|>c

2 sin <() - sin 2<j>o

(ii). The four probe reflectometer

With a fourth equally spaced probe it is also possible to determinethe frequency. (The solution with unequal spacing is somewhat intractable,unless a best fit is found by iterative testing of different frequencieson a digital computer.) By advancing the subscripts in Eq. (26) to includea fourth probe:

(27) D =(P2 + P4) sin sin

2 sin <j> - sin 2<j>

48

Equating the numerators of Eqs. (26) and (27) yields

(28) cos <frs = 1/2

Then if "a" is the probe spacing:

(29) *s =- and

(30) x = 4ira

where x is the wavelength in the transmission line, or the guide wave-length in waveguide.

In a practical ref1ectometer a few restrictions must be imposed toavoid ambiguities and to obtain acceptable accuracy. From Eq. (28)it is evident that as long as (|>s remains in the first two quadrants noambiguity arises in determining x. However, if $$ may possibly exceedIT then there is more than one solution to Eq. (30). Thus, it is necessaryto impose the restriction that:

or

It is worth noting that this condition includes the stipulation madeat the outset that for a three probe ref1ectometer no two probes shallbe spaced at a multiple of x/2, a condition which makes A, B, and Dindeterminate. In the case of four probes it is possible for the firstand fourth probe to be spaced at x/2 apart and still satisfy theseconditions provided that both the first and fourth are not included inthe calculation of A, B, and D.

49

The condition that <|>s be less than TT may be relaxed if theapproximate frequency is known since the correct quadrant for <j>s maythen be determined in advance. In this case there is, in fact, anadvantage in using large probe spacings in that it permits a pro-portionately more accurate frequency determination. Where the frequencyis unknown two sets of probes; one at close spacing and one at widespacing could be used to achieve the same end.

One further limitation exists and that is that if either a maximumor minimum of the standing wave pattern is located exactly midway betweenthe second and third probes the frequency becomes indeterminate. Thisrestriction does not apply if the frequency is already known or ismeasured independently.

In addition to these theoretical limitations there are somepractical limitations which should be observed if accurate measurementsare to be made. The frequency measurement tends to be inaccurate if thereflection coefficient is very small. In this event it is desirable eitherto measure the frequency independently or temporarily to introduce somemismatch to facilitate a frequency reading and then to remove it again forthe reflection measurement. A further limitation is that if "a" is verysmall or approaches A/4 the accuracy will be impaired. Maximum sensitivityexists for a = x/8. A three to one bandwidth is obtainable for "a" betweenA/16 and 3A/16 and a wider band could be used with care.

(iii) Self checking systems

So far only systems employing the minimum number of probes havebeen discussed: three if the frequency is known, four if it is not. Byusing additional probes it is possible to introduce a degree of redundancyand to make the system self checking.

Consider a system in which the frequency is known but in which fourprobes are used. It is possible to calculate V2, p and e in four dif-ferent ways using the probe outputs three at a time. Equations (13),(14), and (15) must be used since only two of the four combinations ofprobes are equally spaced. If the four results agree within acceptablelimits, it is reasonable to assume that the measurement is accurate. Caremust of course be taken in the practical application of this assumption.If for example, a common amplifier is used to monitor the probe outputs,a slow drift in gain could result in an error in V2 while still yieldinga self consistent set of results, p and e would be correct in this case.A fast drift, that is one which changes between reading one probe andthe next, would produce inconsistency in the outputs and hence bedetected. Similarly a defect in one probe, with the others operatingcorrectly, would be detectable, as also would a frequency error.

One extra probe provides the means of detecting errors but notof isolating them. In the case just discussed a defective probe wouldproduce one correct set of outputs and three incorrect sets. It wouldnot, however, be possible to identify the correct set. By introducing

50

a fifth probe in a system where the frequency is known it is possible toobtain ten sets of VS p and e. Four of these do not use the outputfrom any one probe. Thus, if four sets are self consistent eno' theremaining six are not it is possible to identify not only the correctdata but also the defective probe.

When some or all of the data sets agree within acceptable limitsit is possible to improve the accuracy of the final result by averagingthe values for V2 and the reflection coefficient; the reflection coef-ficient is averaged by treating p and e as a single complex quantity.This process, in effect, minimizes the mean square error in the observedstanding wave voltages (Vp).

Similar arguments can of course be applied to systems where thefrequency is regarded as an unknown. It must be remembered that therules regarding probe spacing must be applied to all combinations ofprobes used in self checking.

In the present application four probes are used, the frequencybeing known. Equations (13), (14), and (15) have been programed on acomputer. In making measurements the probe output is read for each ofthe four positions and the readings entered into the computer. Fourvalues for the reflection coefficient are calculated and averaged.In addition the maximum deviation between this average and any of theindividual calculations is found. The average is plotted on a SmithChart by the computer and an error circle, whose radius corresponds tothis maximum deviation, is drawn around it. All the impedance datapresented in this report were obtained in this manner. The errorcircle is a direct indication of the self consistency of the experi-mental data.

As a further check on the accuracy of this method one of theantennas was connected to the ref1ectometer and its impedance measured.A series of waveguide spacers Xg/32 thick were then introduced betweenthe antenna and the ref1ectometer. The result is shown in Fig. 42.With an ideal probe section, this data would fall on a circle whosecenter is at the center of the Smith Chart and whose radius is thereflection coefficient of the load. In any practical measuring systemthe points will fall on a circle whose center is displaced from thecenter of the Smith Chart. The distance from the chart center to thedata circle center is a measure of the reflections from the probesection itself (due to presence of the probe, flange alignment, etc.),i.e., the residual reflections. These measurements indicated a residualVSWR of

VSWR— % 1.008.

VSWRmin

This residual VSWR is close to that attainable with the best coaxialslotted line available and in practice represents a considerable im-provement over such a line since 7 mm connectors typically have VSWR's

51

Fig. 42. Residual VSWR measurement for the 4 probe reflectometer(circular waveguide model).

52

of the order of 1.02 and waveguide to coaxial adapters are usuallymuch worse (typical manufacturer specs "less than 1.25:1").

One further comment should be made in connection with theaccuracy of this technique. An examination of the sensitivity ofthe reflection coefficient to errors in probe voltages was made bydifferentiating the expressions for V2, p and e with respect to oneof the probe outputs. It was observed that the derivatives of e andof the product term pV2 were well behaved but the derivatives of pand V2 separately were proportional to 1/1-p. The accuracy withwhich p and V2 can be determined decreases with increasing p; andthus the method appears unsuitable for measuring anything but thephase angle of loads approaching p = 1. However, since it was plannedto measure the resistive loss in the various antennas by closing themwith a metal cap and observing the resulting reflection coefficient itwas imperative to find a way around this restriction. A closer lookat the derivatives in question showed that they were also proportionalto the distance from the minimum of any two out of a group of threeprobes. This is because of the uncertainty of determining the exactdepth of the minimum with a single probe on a steeply sloping standingwave. Placing two probes near the minimum takes care of this un-certainty. (Alternatively a single probe may be placed exactly atthe minimum, in which case of course it provides the level of theminimum point directly, the other probes providing the remainder ofthe information.) Thus it is still possible to obtain accuratemeasurements for the higher VSHRs. In measuring high reflection coeffi-cients for resistive loss determination, the procedure adopted was toplace one of the probes at the standing wave minimum by using waveguidespacers (variable in AQ/32 steps) and making a final adjustment byvarying the frequency slightly, since the exact frequency of the meas-urement was generally not critical. To avoid problems with the crystallaw a precision attenuator was placed in the feed line to the reflectom-eter in addition to a fixed attenuator pad in the circular waveguidebetween the probe section and the feed point. When the probe was movedto the high level positions attenuation was inserted to bring the probeoutput back to the same level. The attenuator readings were then usedto calculate the reflection coefficient. An alternative method whichwas found to give very similar results was to use an r.f. coupledprobe and a precision receiver.

B. Impeda nce Measurements

Reflection measurements were found to be quite straightforwardusing the four probe technique and measurements of the S-band antennaswere made using the appropriate square or circular probe section. Meas-urements were not made on the square X-band horns because a probesection was never constructed for this guide size. The frequency wasalways measured independently with a cavity wavemeter so that the fourthprobe provided the necessary redundancy for checking the accuracy of themeasurement. The results are shown in Figs. 43-45.

53

Fig. 43. Impedance of the conical corrugated horn, first two slotscovered. (The numbers next to the points arefrequencies in GHz).

54

Fig. 44. :

55

Fig. 45. Impedance of the conical dual mode horn. (The numbersnext to the points are frequencies in GHz).

56

The VSWR of the conical corrugated horn is already below 1.1 in thefrequency range 3.8 to 4.0 GHz thus the reflection loss is less than 0.01dB. With some matching this range could probably be extended since theimpedance points are all to one side of the circle. In any case with theaccuracy obtained (the circles in the figure indicate the uncertainty inthe measurement) the reflection loss, even where greater than 0.01 dB isknown to well within the required accuracy.

The impedance of the pyramidal corrugated horn (Fig. 44) is lesssatisfactory. However, this particular antenna was also unsatisfactoryas regards its radiation pattern characteristics.

Between 3.7 and 4.0 GHz, where its pattern characteristics weremost satisfactory, the conical dual mode antenna shows a VSWR of between1.1 and 1.17 (Fig. 45). Thus the loss is a little over 0.01 dB. Thiscould probably be improved by matching. Again, however, the accuracywith which this loss is known is well within the required limit.

C. Resistive Loss Measurements

A number of methods for measuring the resistive loss in the hornwalls were tried. All of them involved closing the aperture of theantenna with a short circuiting cap. Since it was desired that thereflected fields should be nearly identical to- the incident fields toavoid introducing other modes, the ideal cap should match the phasefront at the aperture. As aperture field measurements had shown thephase front of the conical corrugated horn to be almost perfectlyspherical it was selected for the first tests. The less regular phasefronts of the other antennas would have made construction of a matchingreflector extremely difficult. Accordingly a spherical end cap wasbuilt for the conical corrugated horn.

The first method tried for measuring loss was to make the shortedantenna into a cavity. This was achieved by adding a transition torectangular waveguide and a sliding short circuit. A loosely coupledprobe was then used to excite the cavity and to measure its Q factor,by observing the location of the sliding short circuit at the halfpower points either side of the resonant position. However, it wasfound that the loss in the sliding short-circuit was much greater thanthat in the antenna and also rather unstable. This method was thereforeabandoned.

The next approach was to look for a method of measuring the re-flecion coefficient of the shorted antenna. The loss in reflectedpower in this situation will then be twice the loss in the forwardpower if the antenna were radiating. It has already been stated thatthe multiprobe reflectometer is not suitable for measuring very highreflection coefficients unless two of each group of three probes areclose to the minimum point. This means that three out of four probesmust be close to the minimum if the self checking capability is to beretained. The method shown in Fig. 46 was therefore devised. It was

57

assumed that to a first approximation the change in the standing wavevoltage near the minimum would be the same if either a single testprobe were moved slightly along the waveguide or the probe were leftfixed and the frequency changed by a very small amount. Using a phaselocked transmitter with a frequency offset capability it was possibleto vary the frequency precisely over a range of ±1 MHz around thecenter frequency. One of the four original probe positions wastherefore placed near a standing wave minimum by suitable choiceof frequency and the available waveguide spacers. This singleprobe was then measured as if it were a multiple probe by varyingthe frequency. Additional measurements were also taken for theother probe positions which were of course away from the null.The reflection coefficient was then calculated from the resultingprobe outputs.

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Satisfactory measurements were obtained by this method, however,there were some reservations regarding its use. At some frequenciesspurious nulls were observed on the standing wave pattern due to re-flections from the throat of the horn (Fig. 47). Such nulls do notof course exist on the fixed frequency standing wave pattern but

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only on the psuedo standing wave produced when the frequency ischanged. It was not difficult to distinguish the one null from theother. However, when they occurred close together there was someconcern that there might be distortion in the shape of the true null.It was found that this problem could be avoided if the waveguide spacersand fine frequency control were used only to place one of the probepositions exactly in the null (care had still to be taken to avoid thespurious nulls). The four probe positions were then read in theusual way except that a precision attenuator was used to measure thelevel for the null position by the substitution method, thus avoidingexcessive dependence on the crystal law. The advantage of the redundantfourth probe is lost with this method. However, repeatability of resultsand the fact that the same detector is used in each of the four probepositions gave a high level of confidence to the results.

The measured data for the two conical horns is shown in Fig. 48.The loss shown in the figure is half the measured loss, in other wordsit is the one way loss which would exist with the antenna radiating.The loss of the shorted waveguide is also shown. If the loss in thisshorting plate is assumed to be equal to that in the antenna shortingcap; the waveguide is common to both measurements; then the antennaloss is simply the total loss observed minus that for the shortedguide. The shorted guide showed a loss of 0.0065 dB. The conicalcorrugated horn was measured with both the spherical cap and a flatshorting plate to determine how much the plate contour affected theloss measurement. The loss curve shifted up by 0.0025 dB for the flatplate if one ignores the two high points around 3.75 GHz in Fig. 48,which are assumed to be due to excitation of some higher order modeby the flat plate. Taking the extreme variations for the conical cor-rugated horn (including both shorting plates except for the two pointsnear 3.75 GHz) and subtracting the loss for the shorted guide gives aresultant loss for the horn of 0.016 dB ± 0.0058, well within therequired accuracy of 0.01 dB.

Since the shape of the shorting plate had been found to make onlya minor difference in the loss measurement for the conical corrugatedhorn and because of the complex phase front of the conical dual modehorn it was felt that the use of the flat plate was justified in thiscase. The results for the conical dual mode horn are also shown inFig. 48. Performing the same calculation as before gives a loss of0.0125 dB ± 0.0033.

Similar data for the pyramidal dual mode horn are shown in Fig. 49.A flat shorting plate was again used and it is evident that more of amoding problem existed for the square geometry both for the horn andwaveguide alone. If one assumes that the high loss points are theresult of modes which would not exist in the radiating condition thenthe results are very similar to those for the conical horns. If theworst possible interpretation is put on the data then the horn loss isstill no worse than 0.02 dB ± 0.01.

60

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62

D. Beam Efficiency Measurements

The major problem in determining beam efficiency is the same asthat in calculating directivity from radiation pattern measurements.It is first necessary to record sufficient radiation patterns to givean adequate three dimensional representation over the complete sphere.The recorded patterns must then be integrated as a function of anglefrom the beam axis to provide the data necessary for an efficiency cal-culation. In the present program, with several types of antenna beingevaluated, the number of radiation patterns to be recorded is formidablein itself. Integration of the patterns becomes impracticable unlessboth reading of the patterns and the integration can be performed witha digital computer. Accordingly it was decided that the pattern datashould be recorded directly into an instrumentation computer in realtime without any intermediate pattern recordings. Once in the computera conventional pattern plot, on any desired scale, could readily be ob-tained by outputting the stored data to an X-Y plotter. The data werealso immediately available for any desired computation. The patternrecording and data processing system is illustrated in Fig. 50.

All pattern recording and data processing is performed by a singlecomputer program on command from the teletype. Eighteen commands arecurrently recognized by the program. In operation two calibrationpoints are first given to the computer using the precision attenuatorin the transmitting arm (Fig. 50) and with the receiving antennastationary. In the record mode the computer senses the pedestalrotation through a microswitch which opens and closes for every degreeof rotation. At each switch closure the computer records the receiveroutput. The process continues until 360 points have been recorded.The receiver has a dynamic range of only 40 dB. Since patterns with adynamic range of 50 dB or greater are required for the present purposethe parallel polarized pattern is recorded in two stages. The patternis first recorded with 20 or 30 dB of attenuation in the transmitter.This provides the main beam information. The attenuation is thenremoved (the amount being indicated to the computer via the teletype)and a second pattern is recorded. The receiver will now saturate inthe main beam. The computer automatically merges the two patterns intoa single extended range pattern. At this point the pattern may besmoothed, normalized or centered (if recording was not started at thecenter of the main beam) on command from the teletype and written onthe disc file. If the cross polarized pattern is required, it is recordednext. This may be done with any appropriate attenuator setting at thetransmitter. The pattern will be kept in its correct relationship tothe parallel polarized pattern by the computer. Both the transmittingand test antennas are now rotated about their axes and a second set ofpatterns recorded. In the present work patterns were recorded every22% degrees.

63

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64

Patterns may be drawn on the X-Y plotter at any time using anydesired scale limits. They may be superimposed on the same plot inany combination. When a complete set of patterns is stored on thedisc file they may be analyzed to obtain the beam efficiency. Thepatterns are first averaged, parallel and cross polarization beingtreated separately. If the cross polarized energy is to be treatedas desirable it is added to the parallel polarized pattern at thispoint and the resulting pattern renormalized. The analysis sectionof the program is then invoked and the parallel and cross polarized(if being treated as undesirable) file names entered. The patternsare now integrated and an efficiency curve calculated expressed aspercent of power within a given angle from the beam axis. This curvemay be plotted or stored on the disc. Half power beamwidth, directivityand efficiency at twice the half power beamwidth are printed on theteletype.

This last parameter has been used in this program as a figure ofmerit for the antenna since the patterns in general do not have sharpnulls and hence a well defined beam edge. Examination of the efficiencycurves suggests that it may not, however, be the most appropriatefigure. The curves for the horn antennas exhibit a definite knee around97%. This knee could be identified mathematically as the point wherethe curvature is sharpest (i.e., the second derivative highest). Itmay well be that this is the point that should be defined as the beamedge for radiometer antennas, the efficiency at this point would then bea more realistic figure of merit.

V. NEAR FIELD STUDIES

During this program the possibility was raised of using the hornantennas, which had been developed, for radiometeric studies of waterin a ripple tank. As it was thought possible that the antennas mightbe used under near field conditions some measurements were made toevaluate the near field properties.

In the case of the two conical horns it was found that theirradiation patterns remained essentially the same as in the far fieldfor ranges down to about 30 inches or 3 aperture widths. (The usual2D^/x criterion for this antenna gives a far field range of 66 inches.)To demonstrate the near field effect patterns were accordingly measuredat one third and two thirds of this distance or 10 and 20 inches. Thesepatterns together with the beam efficiency curves are shown in Figs. 51-62. The cross polarized radiation has been treated as undesirable inthe efficiency calculations.

For comparison purposes similar measurements were made on a 2 footdiameter paraboloid operating at 10 GHz. This is not the same paraboloidas that shown earlier in this report. Since the measurements were madeindoors it was not possible to satisfy the usual far field criteria.

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The maximum range available was 28 feet. The patterns and beam efficiencycurve at this range are shown in Figs. 63-65. The beam efficiency shouldbe regarded with some reservations since the beam width of this antennawas 4 degrees and the computer only samples the pattern at a rate of1 point per degree. Patterns at ranges of 7.5 feet and 2.7 feet areshown for this antenna in Figs. 66-71. Here the beam has broadenedsufficiently that the efficiency calculation should be accurate.

In addition to the near field amplitude measurements of the cor-rugated and dual mode conical horns (Figs. 51-62) some phase patternswere also recorded. An open-ended rectangular waveguide was used asthe transmitting antenna. For some of the patterns the test antennawas rotated about an axis through apex of the horn and for othersabout an axis in the aperture plane (Fig. 72). The resulting phasepatterns are shown in Figs. 73-77.

VI. RADOME LOSS MEASUREMENTS

Another question arose during this program, namely the effectof a radome on the antenna system losses. If the antenna is to beused for radiometric studies aboard an aircraft it is necessary thatit be covered with a radome to protect it from weather and to preservethe aerodynamic contour of the aircraft. The major concern here was notany loss which might originate in the radome itself since this could bemeasured and calibrated out if it proved to be significant. More un-certain was the loss due to rain, oil or dirt deposits on the radome.

To investigate this problem an experiment was set up as shown inFig. 78. It consists of a conventional waveguide slotted line terminatedin a short circuit. One quarter of a guide wavelength from the shortcircuit, which was easily removable, was a thin mylar diaphragm clampedbetween two waveguide flanges. The system was operated vertically withthe short uppermost. On top of the mylar was placed a rectangle offilter paper cut to fit the waveguide. The filter paper was weighedon a chemical balance having first been heated to drive out anyresidual moisture. It was then moistened with water, and weighedagain, the object of the filter paper being to ensure a uniform distri-bution of water. As quickly as possible it was placed in the waveguideand a VSWR reading taken. The waveguide was then opened and the filterpaper allowed to dry slightly. It was weighed again and another VSWRmeasurement taken. This process was repeated until the paper was com-pletely dry. The loss in reflected power was calculated from the VSWRreadings. Since the water is at a standing wave maximum and couplesonly to the E-field the observed loss will be four times what it wouldbe if the same forward power were being transmitted into a matched load.Thus a quarter of the observed loss was plotted against the amount ofwater on the filter paper (Fig. 79). The fact that coupling was onlyto the E-field was verified by placing half a wavelength of waveguidebeyond the diaphragm and repeating the measurement. No increase inloss was observed in this case when water was added. The same meas-urement was repeated using lubricating oil on the diaphragm.

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A similar set of measurements of VSWR were then made with theshort circuit replaced by a precisely matched load (Fig. 80). Theobject of this measurement was to see if there was correlation betweenreflection and loss due to the radome.

Following this initial test the next step was to repeat themeasurements for an antenna. The conical dual mode horn was selectedfor this purpose because of its smaller flare angle. An open web ofnylon threads was constructed a quarter wavelength from the aperture bydrilling small holes through the horn walls for attachment purposes.The guide wavelength for the modes of interest is very nearly equal tothe free space wavelength at this point in the horn. The horn wasmounted vertically and a mylar diaphragm and filter paper were placedon the supporting web. The horn mouth was closed with a flat plateand VSWR measurements were made, as in the earlier loss measurementson this horn, using the four probe ref1ectometer in circular waveguide.Similar data were taken for various amounts of water on the filter paperas had been done in the rectangular guide. The oil measurement wasomitted this time as it was felt that the initial tests had shown thisto produce negligible loss. The comparative results for the horn andrectangular guide for the case of water are shown in Figs. 81-82. Topermit a direct comparison the water density has been expressed inmilligrams per 3.8 sq. in. of area (i.e., the area of the rectangularguide). Some difference may be seen between the two cases but this isto be expected since the modes are not identical.

The next question considered was the possible effect of contaminationin the water, particularly due to salt spray. The horn measurements weretherefore repeated using distilled water and a salt solution. Tap waterwas used for the first measurements. The three results are compared inFigs. 83-84. Because of the difficulty of controlling evaporation overthe large area of filter paper a uniform salt concentration was notmaintained. Instead a 0.3 molal solution was prepared initially. Thepaper was then allowed to dry as before to obtain successive readings.Thus the amount of salt remained constant but the concentration in-creased. The total amount of salt present is indicated by the intercepton the horizontal axis of Fig. 83 after the water had evaporated, thedry salt producing negligible attenuation.

In order to determine whether or not it is possible to measureradome loss in flight by monitoring the VSWR, the transmission loss andVSWR, for various conditions of the horn window, were plotted againsteach other in Fig. 85. It is evident that if the water is pure ornearly so a definite relationship exists between the loss and VSWR.However, if an unknown amount of salt is present it is not possibleto infer the one from the other. Nevertheless, if the radome isinitially clean it should be possible to estimate the loss due torain on the window by a VSWR measurement if the distribution of wateris fairly uniform.

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One further form of possible contamination was investigated briefly.The mylar window in a rectangular waveguide was first smeared with oil.The window was then covered with "road dust" and as much dust as didnot adhere to the oil was blown off. The general appearance of thewindow is illustrated qualitatively in Fig. 86. Carbon scraped fromthe tail pipe of an automobile was added to the dust for some tests.The highest equivalent radome loss observed was about 0.005 dB whichmay be considered negligible.

99

Fig. 86. Approximate appearance of the waveguide window whencoated with oil and road dust.

VII. GEOMETRICAL DIFFRACTION THEORY APPLIEDTO DUAL MODE HORN DESIGN

In order to provide a better insight into the operation of thevarious horn types and ultimately to develop design procedures andmake loss estimates for the dual mode geometries without resortingto empirical techniques, the geometrical theory of diffraction hasbeen applied to the dual mode horn structures.

The geometric theory of diffraction analysis of the near fieldsof the dual mode horns has yielded some useful results but has provedto be rather cumbersome because of the large number of rays whichmust be considered in the analysis. The calculated aperture distri-bution for the pyramidal dual mode horn agrees fairly well withmeasured results in both the E-plane and H-plane. The conical dualmode horn analysis has not been completed but should yield similarresults since the analysis is similar to the pyramidal dual mode horn.An outline of the analysis and some initial results appear here. Amore detailed discussion of this work along with computer programsand additional calculated results will appear in a future report.

100

A. The Pyramidal Dual Mode Horn

The horn considered is composed of two pyramidal sections separatedby a mode generating step discontinuity. The slant length of the twosections is 8.39 cm for the section between the waveguide and the stepand 36.3 cm for the other section. The step height is 1.03 cm and theflare angle of each section is 10°. The computations have been madeat a wavelength of 8 cm (3.75 GHz) to obtain both the E-plane and theH-plane aperture distributions. The fields incident on the horn-waveguide junction are assumed to be due to the dominant TEn-i wave-guide mode propagating in a square waveguide 4.42 cm on a side. In theE-plane, this mode is represented as a TEM wave propagating along the axisof the waveguide while the H-plane representation is the familiar planewave pair bouncing between the waveguide walls. Figures 87 and 88 showthe incident rays considered in the H-plane and E-plane respectively.The incident field at an edge is a combination of the diffracted fieldsfrom all the other unshadowed edges plus the direct waveguide incidentfield, if it is not shadowed. These incident rays after diffractingat the edge combine to form the internal horn fields. The rays usedto determine the aperture fields in both the E- and H-plane are shownin Fig. 89 for a typical observation point. The various forms of theVB diffraction coefficient7 were used in computing the aperture distri-butions shown in Figs. 90 and 91. Figure 90 shows measured and calculatedaperture fields in the H plane along with a cosine distribution forcomparison, since the H plane fields should be nearly cosinusoidal. Themeasured data were obtained using a nulled backscatter system and movinga very small sphere across the aperture and recording the relative levelof the reflected signal. The corresponding E-plane results are shown inFig. 91. Here the cosine distribution is shown just for comparison withthe H-plane data. While the agreement between measured and calculatedH-plane aperture distributions is excellent, the agreement in the E-planeis only fair. This is not too surprising since the E-plane is the onewhere the mode generating step is effective and the small height of thestep (^ x/8) makes the G.T.D. analysis somewhat questionable even whenthe near field form is used for the interaction between the two wedgeswhich form the step. These results, however, should be adequate for anapproximate loss calculation.

B. The Conical Dual Mode Horn

The conical dual mode horn considered here is the same one treatedelsewhere in this report. The slant length anfd flare angle of theconical section between the 2.8 cm radius circular waveguide and themode generating step are 6.0 cm and 10.4° respectively. The secondconical section has a 39 cm slant length with a 10.4° flare angle andis separated from the first section by a 1.0 cm (x/8) step (x = 8 cm,f = 3.75 GHz). The circular waveguide is operated in its dominantmode which may be represented as a conical bundle of plane wavesemanating from the waveguide axis. In a given plane containing thewaveguide axis, this mode picture is similar to the plane wave pairpicture usually associated with the H-plane of the TEgi rectangularwaveguide mode. Details of this analysis and computed results willappear in a future report.

101

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VIII. CONCLUSIONS

This work has shown that the criteria for the design of highperformance radiometer antennas are considerably different fromthose for communications antennas. Of major importance is the radi-ation pattern which must have very low side and backlobes. It hasbeen shown that the popular "half-power-beamwidth" has little meaningfor a radiometer antenna nor does the full beamwidth in radiation patternswhich have essentially no nulls. Rather the beamwidth should be definedin terms of the fraction of the radiated power (the antenna consideredas transmitting) contained within a given angle. Beam efficienciesbased on this definition have been measured for a number of horn antennas.The efficiency curves exhibit a natural knee around 97% efficiency wherethe second derivative of included power versus angle from the beam axisreaches a maximum. This would seem to be a logical point to define asthe beam edge, the included power at this point being a figure of merit

106

for the antenna. The antennas designed and tested under this program,namely pyramidal and conical horns using both corrugated walls and dualmode techniques to produce the required beam shape, have proved farsuperior to such conventional antennas as the paraboloid.

In addition to having a clean radiation pattern it is essentialthat the reflection coefficient and wall losses of a good radiometerantenna be low. More important still is to know the residual lossesto a high degree of accuracy so that correction can be made. Multi-probe ref1ectometer techniques have been developed under this programto the point where it is possible to measure these losses to betterthan 0.01 dB of the forward power when the antenna is transmitting.This is better than 1°K for a radiometer antenna if the losses areassumed to occur at an ambient temperature of 300°K. This techniqueavoids the need to construct special slotted lines for the circularand square waveguides used and also avoids the unacceptable approach,when this sort of accuracy is needed, of using a transition to a con-ventional sized slotted line.

The program has also seen the development of the geometrical theoryof diffraction to the point where it is possible to calculate radiationpatterns for dual mode horn geometries. This should permit future designswithout the need for empirical adjustment of the mode forming system.The method also offers promise for calculating reflection and absorptionlosses directly.

While the program has produced major improvements in antenna designfor radiometer applications, the antennas developed have been relativelylow gain. Future work should be directed towards more directive antennasystems. Such systems might include the horn reflector antenna whichoffers no benefit in low gain systems. The techniques so far developedoffer many possibilities for improving higher gain systems.

107

REFERENCES

1; Lawrie, R. and Peters, L., Jr., "Modification of Horn Antennasfor Low Sidelobe Levels," The Ohio State University, IEEE -GAP, September 1966, Vol. AP-14, No. 5.

2. Narashimhan, M.S., "Corrugated Rectangular Horns," personalcommunication.

3. Jeuken, M.E.J., "Frequency Independence and Symmetry Propertiesof Corrugated Conical Horn Antennas with Small Flare Angles,"Theoretical Electrical Engineering Group, Eindhoven Universityof Technology, Eindhoven, The Netherlands, 8 December 1970.

4. Clarricoats, P.J.B., "Analysis of Spherical Hybrid Modes in aCorrugated Conical Horn," Electronics Letters, 1 May 1969,Vol. 5, No. 9, p. 189.

5. Potter, P.O., "A New Horn Antenna with Suppressed Sidelobesand Equal Beamwidths," Microwave Journal, June 1963, pp. 71-78.

6. Jakes, W.C., Jr., "Horn Antennas," in Jasik, H., editor,Antenna Engineering Handbook, McGraw-Hill Book Co., 1961,pg. 10-12.

7. Rudduck, R. and Tsai, L.L., "Application of Optical Methods toMicrowave Problems," Short Course 1969, Department of ElectricalEngineering, ElectroScience Laboratory, The Ohio State University,section IV.

108

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